Hey, I just noticed that a lot of the mechanisms of heating that I've been talking about are also explained similarly on that American Institute of Physics site that I cited in my second post to this thread.
http://www.scienceagogo.com/forum/ubbthreads.php?ubb=showflat&Number=26109#Post26109I should have looked at that 'aip' site earlier, and just quoted stuff from there rather than composing an explanation out of what I recalled from my college days.
http://www.aip.org/history/climate/simple.htm#L_0141"It appeared that there was already enough CO2 in the air so that its effect on infrared radiation was "saturated" — meaning that all the radiation that the gas could block was already being absorbed, so that adding more gas could make little difference. Moreover, water vapor also absorbed heat rays, and water was enormously more abundant in the atmosphere than CO2. How could adding CO2 affect radiation in parts of the spectrum that H2O (not to mention the CO2 itself) already entirely blocked?
These studies with the crude techniques of the early 20th century were inaccurate. Modern data show that even in the parts of the infrared spectrum where water vapor and CO2 are effective, only a fraction of the heat radiation emitted from the surface of the Earth is blocked before it escapes into space. And that is beside the point anyway. The greenhouse process works regardless of whether the passage of radiation is saturated in lower layers. As explained above, the energy received at the Earth’s surface must eventually work its way back up to the higher layers where radiation does slip out easily. Adding some greenhouse gas to those high, thin layers must warm the planet no matter what happens lower down."
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Looking back, some more, I see your were always talking natural logs. What about the mikechurch (yellow) graph?
What about your formula from:
http://motls.blogspot.com/2008/01/why-is-greenhouse-effect-logarithmic.html[-a deadly site- you'll be snow-blind after reading one paragraph -from the actual 'black' page]
"With the assumptions listed above, and they are kind of - although not perfectly - satisfied for the doubling from 280 to 560 ppm of CO2 as one can check (the temperature change comparable to 1 °C is much smaller than the 300K absolute temperature, the percentages change from 92:8 to 95:5 or something like that is relatively small), the Arrhenius' law is a law. It is all about the Maxwell-Boltzmann distribution, the lapse rate, and the black body law. A geometric/exponential increase of the concentration moves the physical phenomena linearly in altitude and makes standardized linear contributions to various terms."
This is gibberish, isn't it?
Ow, my eyes! I had to look at that site again to get this.
"Phenomenologically, the linear increase for small C and the logarithmic law for the large values of C is often interpolated by a function that is also quadratic in the middle but it is just one of possible conventions for curve-fitting. Another popular function is
Temperature = Temperature0 + ln(1 + 1.2 x + 0.005 x2 + 0.0000014 x3)
where "x" is the CO2 concentration in ppmv. This formula works pretty well up to 1,000 ppmv.
However, the asymptotic logarithmic behavior for large C is more than a convention. It can be derived as a result of an idealized calculation that is relatively realistic - a kind of calculation that theoretical physicists, especially condensed-matter physicists, should like. One reason for the logarithm could be found if we were looking how new spectral lines and their "wings" become relevant for the absorption. The old lines eventually get saturated but the total greenhouse warming never quite stops because new spectral lines emerge: it just slows down...."
Holy Crap! Talk about gibberish....
And that formula is the one I said somebody had switched Absorption and Temperature (and relabeled the graph).
Uncitable concoction, I still maintain.
Now, your chart/graph John, (thanks for all your time making that work, btw) as you say is similar because it has a ln factor. Especially if you plot absolute change in concentration instead of the change ratio. You've simply repeated the Motl (now I know who that is) graph by plotting the preceding concentration subtracted from the successive concentration, haven't you?
Or... why doesn't 2 ppm give almost infinite Forcing???
IMHO
Your x axis should go from zero to five(ish), to represent the Concentration
ratio of C/Co (i.e. 560/280 would be 2 on the x axis, or 350/280 would be 1.25), and could then be plotted against the delta F (change in Forcing from the initial forcing of Co).
This way also, if you looked at 200ppm/280ppm, the natural log would be negative (showing the lowering in forcing relative to the initial forcing of Co at 280ppm.
I think that is what the ΔF = α ln(C/C0) equation is trying to show.
Does that make sense?
Thanks again,
~Later
